Quaternionic Analysis and the Algebrodynamics

Details Quaternionic Analysis and the Algebrodynamics Quaternionic Analysis and the Algebrodynamics

2007-10-15

arxiv.org/abs/0710.2895v1

In: "Space-Time Structure. Algebra and Geometry", eds. D.G.Pavlov, Gh. Atanasiu, V.Balan. -- Moscow: Lilia-Print, 2007, pp. 44

Physics

Mathematical Physics

32 pages, 1 figure

Scientific paper

We present the ``algebrodynamical'' approach to field-particle theory based on a nonlinear generalization of the Cauchy-Riemann conditions to non-commutative algebras of quaternion-like type. For complex quaternions the theory is Lorentz invariant and naturally carries some gauge and twistor structures. Point- and string-like singularities are considered as particle-like formations; their electric charge is ``self-quantized''. A novel ``causal Minkowski geometry with additional phase'' is presented that is induced by the structure of primordial biquaternion algebra. On this geometrical background a self-consistent algebraic dynamics of singularities (``ensemble of dublicons'') is briefly discussed.

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